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# Exploring the concept of Test Accuracy Ratio (TAR) and Test Uncertainty Ratio (TUR)

Updated: Sep 13

For every measurement, the answer to the question of how “good” a measurement needs to be to meet a particular specification is often dictated by what is called ‘Decision Rules.

TAR (Test Accuracy Ratio) and TUR (Test Uncertainty Ratio) are the industry's top accepted decision rules. To better understand these terminologies, we need to familiarise ourselves with some basic concepts, such as:

1. What is Accuracy?

The accuracy of a measuring instrument is the indication of the ability of a measuring instrument to give responses close to the true value of the parameter being measured.

2. What is the accuracy of a measurement?

The accuracy of a measurement is the indication of how closely the measurement result agrees with the true value of the parameter being measured.

The true value is always unknown; hence accuracy is always calculated as an estimate, which in turn conforms that accuracy is merely a qualitative value.

To gain a better understanding and give more meaning, accuracy is often defined with information regarding the uncertainty of the measuring system.

3. What is Uncertainty?

Uncertainty lays out the range of probable values for the parameter being measured, with a specified level of confidence. To better define, it is the cumulative ‘accuracies’ of the variables involved in the measurement, that ensures the measured values lie within given boundaries.

Now that we are familiar with the terms, let us move on to what TAR is.

TAR= Tolerance of the unit under test(UUT) / Accuracy of the reference standard.

TAR embodies the usage of qualitative analysis and deploys accuracy in its calculation, which is merely an indication of the ‘potential quality of the instrument.

The concept of uncertainty and accuracy are often misinterpreted and seem confusing. ISO/IEC 7025 states the importance of calculating uncertainty correctly as a primary requirement when it comes to quality assurance. If not specified in detail, it is often very easy for manufacturers to adopt shortcuts and proceed with relying on accuracy details alone.

This very reason makes it very hard to digest the adoption of still relying on TAR calculation in the industry.

TUR on the other hand = Tolerance of the unit under test (UUT) / Uncertainty of the reference standard ( to be more accurate, Uncertainty of the measurement system as a whole to include contributions of the UUT for repeatability and resolution)

TUR emphasizes the calibration process uncertainty and helps give the end user a ratio that is more reliable and meaningful in terms of implementation.

Let us look at an example of how a real-life scenario calculation is done during measurement.

The TAR is usually expressed as a percentage of tolerance (25%), or a single value (4). Let us consider an example where the TAR is calculated as a single value and is required to be equal to or greater than four.

For the first example, a manufactured part is measured, and the measured feature is a 20 mm diameter shaft with a tolerance of ± 0.015 mm. The measuring instrument is a 0-25 mm outside micrometer, with a specified accuracy tolerance of ± 0.001 mm.

The TAR is calculated as 𝑇𝐴𝑅 = ± 𝑇𝑜𝑙𝑒𝑟𝑎𝑛𝑐𝑒 𝑏𝑒𝑖𝑛𝑔 𝑐ℎ𝑒𝑐𝑘𝑒𝑑/±𝐴𝑐𝑐𝑢𝑟𝑎𝑐𝑦 𝑜𝑓 𝑚𝑒𝑎𝑠𝑢𝑟𝑖𝑛𝑔 𝑒𝑞𝑢𝑖𝑝𝑚𝑒𝑛𝑡

= ±0.015 mm/ ± 0.001 mm = 15

In this first example, the TAR = 15 is acceptable as it is greater than the requirement of four.

Based on this rule, the outside micrometer is an acceptable choice for measuring equipment.

For a second example, let us look at the calibration of this same outside micrometer. The calibration is done using Grade AS-1 gage blocks. The tolerance for Grade AS-1 gage blocks (as per standard) is up to 25 mm i.e. ± 0.30 µm.

The TAR is calculated as 𝑇𝐴𝑅 = ± 𝑇𝑜𝑙𝑒𝑟𝑎𝑛𝑐𝑒 𝑏𝑒𝑖𝑛𝑔 𝑐ℎ𝑒𝑐𝑘𝑒𝑑 /±𝐴𝑐𝑐𝑢𝑟𝑎𝑐𝑦 𝑜𝑓 reference 𝑒𝑞𝑢𝑖𝑝𝑚𝑒𝑛𝑡 = ± 1 μm/ ± 0.3 μm = 3.3

In this case, the TAR = 3.3 is not acceptable, and different gauge blocks should be considered.

This depicts a simple example of how TAR is used in determining decision values.

TUR, the evaluation of measurement uncertainty presented itself into commercial calibration practice in the late 1990s. As more and more calibration laboratories started calculating and documenting uncertainty, the practice of using TAR calculations began to be replaced with the test uncertainty ratio, TUR. The use of simple acceptance and rejection decision rules with TUR requirements is now found in many national and international standards for the calibration of measuring equipment.

TUR is calculated in a similar manner as the TAR; however, an estimate for the measurement uncertainty is needed. For the same micrometer example discussed above – a 0-25 mm outside micrometer is calibrated with Grade 0 gage blocks. In that example, the estimate of the measurement uncertainty is ± 0.25 µm.

The TUR is calculated as 𝑇𝑈𝑅 = ± 𝑇𝑜𝑙𝑒𝑟𝑎𝑛𝑐𝑒 𝑏𝑒𝑖𝑛𝑔 𝑐ℎ𝑒𝑐𝑘𝑒𝑑/ ± 𝑀𝑒𝑎𝑠𝑢𝑟𝑒𝑚𝑒𝑛𝑡 𝑢𝑛𝑐𝑒𝑟𝑡𝑎𝑖𝑛𝑡𝑦 of reference

= ± 1 μm/ ± 0.25 μm = 4

If Grade 0 gage blocks with a tolerance of ± 0.14 µm up to 25 mm are used, the new TAR is calculated as 𝑇𝐴𝑅 = ± 𝑇𝑜𝑙𝑒𝑟𝑎𝑛𝑐𝑒 𝑏𝑒𝑖𝑛𝑔 𝑐ℎ𝑒𝑐𝑘𝑒𝑑 ±𝐴𝑐𝑐𝑢𝑟𝑎𝑐𝑦 𝑜𝑓 𝑚𝑒𝑎𝑠𝑢𝑟𝑖𝑛𝑔 𝑒𝑞𝑢𝑖𝑝𝑚𝑒𝑛𝑡 = ±1 μm/ ± 0.14 μm = 7.1

The TUR ≥ 4 requirement is therefore achieved, and a simple acceptance decision rule can be used. In this example, the TUR = 4 when the TAR = 7.1. Hence, provides proof of why TUR provides more insights than TAR, for a decision value that is close to the expected standards.

Rising industry standards are driving the change by leading the industry to look upon the uncertainty of measurement and thereby adopting TUR over TAR. TUR vouches for better conformity to the industry standards in relation to calibration, wherein the laboratories are required to document the corresponding decision rule that is employed, taking into consideration, and understanding the true purpose of TAR/TUR, which is to prevent false acceptance of nonconforming items. Such mechanisms can help by reducing calibration costs and downtimes.

The decision to use TAR or TUR often lies at the heart of measurement. It is important to clearly define the expectations and terms to further avoid ambiguity!